The insulating, fully ordered, double perovskite Sr2CoOsO6 undergoes two magnetic phase transitions. The Os(VI) ions order antiferromagnetically with a propagation vector k = (1/2, 1/2, 0) below T-N1 = 108 K, while the high-spin CO(II) ions order antiferromagnetically with a propagation vector k = (1/2, 0, 1/2) below T-N2 = 70K. Ordering of the Os(VI) spins is accompanied by a structural distortion from tetragonal 14/m symmetry to monoclinic I2/m symmetry, which reduces the frustration of the face centered cubic lattice of Os(VI) ions. Density functional theory calculations show that the long-range Os-O-Co-O-Os and Co-O-Os-O-Co superexchange interactions are considerably stronger than the shorter Os-O-Co interactions. The poor energetic overlap between the 3d orbitals of Co and the 5d orbitals of Os appears to be responsible for this unusual inversion in the strength of short and long-range superexchange interactions.